Category: Electricity and magnetism

The Crazy Theory contest is still going strong in the back room at Al’s coffee shop. I gather from the score board scribbles that Jim’s Mars idea (one mark-up says “2 possible 2 B crazy!“) is way behind Amanda’s “green blood” theory. There’s some milling about, then a guy next to me says, “I got this, hold my coffee,” and steps up to the mic. Big fellow, don’t recognize him but some of the Physics students do — “Hey, it’s Cap’n Mike at the mic. Whatcha got for us this time?”

“I got the absence of a theory, how’s that? It’s about the Four Forces.”

“Nah, Jennie, that’s Terry Pratchett’s Theory of Historical Narrative. We’re doing Physics here. The right answer is Weak and Strong Nuclear Forces, Electromagnetism, and Gravity, with me? Question is, how do they compare?”

Another voice from the crowd. “Depends on distance!”

“Well yeah, but let’s look at cases. Weak Nuclear Force first. It works on the quarks that form massive particles like protons. It’s a really short-range force because it depends on force-carrier particles that have very short lifetimes. If a Weak Force carrier leaves its home particle even at the speed of light which they’re way too heavy to do, it can only fly a small fraction of a proton radius before it expires without affecting anything. So, ineffective anywhere outside a massive particle.”

It’s a raucous crowd. “How about the Strong Force, Mike?”

. <chorus of “HOO-wah!”>

“Semper fi that. OK, the carriers of the Strong Force —”

. <“Naa-VY! Naaa-VY!”>

. <“Hush up, guys, let him finish.”>

“Thanks, Amanda. The Strong Force carriers have no mass so they fly at lightspeed, but the force itself is short range, falls off rapidly beyond the nuclear radius. It keeps each trio of quarks inside their own proton or neutron. And it’s powerful enough to corral positively-charged particles within the nucleus. That means it’s way stronger inside the nucleus than the Electromagnetic force that pushes positive charges away from each other.”

“How about outside the nucleus?”

“Out there it’s much weaker than Electromagnetism’s photons that go flying about —”

. <“Air Force!”>

. <“You guys!”>

“As I was saying… OK, the Electromagnetic Force is like the nuclear forces because it’s carried by particles and quantum mechanics applies. But it’s different from the nuclear forces because of its inverse-square distance dependence. Its range is infinite if you’re willing to wait a while to sense it because light has finite speed. The really different force is the fourth one, Gravity —”

. <“Yo Army! Ground-pounders rock!”>

“I was expecting that. In some ways Gravity’s like Electromagnetism. It travels at the same speed and has the same inverse-square distance law. But at any given distance, Gravity’s a factor of 1038 punier and we’ve never been able to detect a force-carrier for it. Worse, a century of math work hasn’t been able to forge an acceptable connection between the really good Relativity theory we have for Gravity and the really good Standard Model we have for the other three forces. So here’s my Crazy Theory Number One — maybe there is no connection.”

. <sudden dead silence>

“All the theory work I’ve seen — string theory, whatever — assumes that Gravity is somehow subject to quantum-based laws of some sort and our challenge is to tie Gravity’s quanta to the rules that govern the Standard Model. That’s the way we’d like the Universe to work, but is there any firm evidence that Gravity actually is quantized?”

. <more silence>

“Right. So now for my Even Crazier Theories. Maybe there’s a Fifth Force, also non-quantized, even weaker than Gravity, and not bound by the speed of light. Something like that could explain entanglement and solve Einstein’s Bubble problem.”

. <even more silence>

“OK, I’ll get crazier. Many of us have had what I’ll call spooky experiences that known Physics can’t explain. Maybe stupid-good gambling luck or ‘just knowing’ when someone died, stuff like that. Maybe we’re using the Fifth Force in action.”

. <complete pandemonium>

~ Rich Olcott

Note to my readers with connections to the US National Guard, Coast Guard, Merchant Marine and/or Public Health Service — Yeah, I know, but one can only stretch a metaphor so far.

Suddenly there’s a hubbub of girlish voices to one side of the crowd. “Go on, Jeremy, get up there.” “Yeah, Jeremy, your theory’s no crazier than theirs.” “Do it, Jeremy.”

Sure enough, the kid’s here with some of his groupies. Don’t know how he does it. He’s a lot younger than the grad students who generally present at these contests, but he’s got guts and he grabs the mic.

“OK, here’s my Crazy Theory. The Solar System has eight planets going around the Sun, and an oxygen atom has eight electrons going around the nucleus. Maybe we’re living in an oxygen atom in some humongous Universe, and maybe there are people living on the electrons in our oxygen atoms or whatever. Maybe the Galaxy is like some huge molecule. Think about living on an electron in a uranium atom with 91 other planets in the same solar system and what happens when the nucleus fissions. Would that be like a nova?”

There’s a hush because no-one knows where to start, then Cathleen’s voice comes from the back of the room. Of course she’s here — some of the Crazy Theory contest ring-leaders are her Astronomy students. “Congratulations, Jeremy, you’ve joined the Honorable Legion of Planetary Atom Theorists. Is there anyone in the room who hasn’t played with the idea at some time?”

No-one raises a hand except a couple of Jeremy’s groupies.

“See, Jeremy, you’re in good company. But there are a few problems with the idea. I’ll start off with some astronomical issues and then the physicists can throw in some more. First, stars going nova collapse, they don’t fission. Second, compared to the outermost planet in the Solar System, how far is it from the Sun to the nearest star?”

A different groupie raises her hand and a calculator. “Neptune’s about 4 light-hours from the Sun and Alpha Centauri’s a little over 4 light-years, so that would be … the 4’s cancel, 24 hours times 365 … about 8760 times further away than Neptune.”

“Nicely done. That’s a typical star-to-star distance within the disk and away from the central bulge. Now, how far apart are the atoms in a molecule?”

“Aren’t they pretty much touching? That’s a lot closer than 8760 times the distance.”

“Yes, ma’am. All electrons have exactly the same properties, ¿yes? but different planets, they have different properties. Jupiter is much, much heavier than Earth or Mercury.”

Astrophysicist-in-training Jim speaks up. “Different force laws. Solar systems are held together by gravity but at this level atoms are held together by electromagnetic forces.”

“Carry that a step further, Jim. What does that say about the geometry?”

“Gravity’s always attractive. The planets are attracted to the Sun but they’re also attracted to each other. That’ll tend to pull them all into the same plane and you’ll get a flat disk, mostly. In an atom, though, the electrons or at least the charge centers repel each other — four starting at the corners of a square would push two out of the plane to form a tetrahedron, and so forth. That’s leaving aside electron spin. Anyhow, the electronic charge will be three-dimensional around the nucleus, not planar. Do you want me to go into what a magnetic field would do?”

“No, I think the point’s been made. Would someone from the Physics side care to chime in?”

“Synchrotron radiation.”

“Good one. And you are …?”

“Newt Barnes. I’m one of Dr Hanneken’s students.”

“Care to explain?”

“Sure. Assume a hydrogen atom is a little solar system with one electron in orbit around the nucleus. Any time a charge moves it radiates waves into the electromagnetic field. The waves carry forces that can compel other charged objects to move. The distance an object moves, times the force exerted, equals the amount of energy expended by the wave. Therefore the wave must carry energy and that energy must have come from the electron’s motion. After a while the electron runs out of kinetic energy and falls into the nucleus. That doesn’t actually happen, so the atom’s not a solar system.”

Jeremy gets general applause when he waves submission, then the crowd’s chant resumes…

Stepping into Pizza Eddie’s I see Jeremy at his post behind the gelato stand, an impressively thick book in front of him. “Hi, Jeremy, one chocolate-hazelnut combo, please. What’re you reading there?”

“Hi, Mr Moire. It’s Moby Dick, for English class.”

“Ah, one of my favorites. Melville was a 19th-century techie, did for whaling what Tom Clancy did for submarines.”

“You’re here at just the right time, Mr Moire. I’m reading the part where something called ‘the corpusants’ are making lights glow around the Pequod. Sometimes he calls them lightning, but they don’t seem to come down from the sky like real lightning. Umm, here it is, he says. ‘All the yard-arms were tipped with pallid fire, and touched at each tri-pointed lightning-rod-end with three tapering white flames, each of the three tall masts was silently burning in that sulphurous air, like three gigantic wax tapers before an altar.’ What’s that about?”

“That glow is also called ‘St Elmo’s Fire‘ among other things. It’s often associated with a lightning storm but it’s a completely different phenomenon. Strictly speaking it’s a concentrated coronal discharge.”

“That doesn’t explain much, sir.”

“Take it one word at a time. If you pump a lot of electrons into a confined space, they repel each other and sooner or later they’ll find ways to leak away. That’s literally dis-charging.”

“How do you ‘pump electrons’?”

“Oh, lots of ways. The ancient Greeks did it by rubbing amber with fur, Volta did it chemically with metals and acid, Van de Graaff did it with a conveyor belt, Earth does it with winds that transport air between atmospheric layers. You do it every time you shuffle across a carpet and get shocked when you put your finger near a water pipe or a light switch.”

“That only happens in the wintertime.”

“Actually, carpet-shuffle electron-pumping happens all the time. In the summer you discharge as quickly as you gain charge because the air’s humidity gives the electrons an easy pathway away from you. In the winter you’re better insulated and retain the charge until it’s too late.”

“Hm. Next word.”

“Corona, like ‘halo.’ A coronal discharge is the glow you see around an object that gets charged-up past a certain threshold. In air the glow can be blue or purple, but you can get different colors from other gases. Basically, the electric field is so intense that it overwhelms the electronic structure of the surrounding atoms and molecules. The glow is electrons radiating as they return to their normal confined chaos after having been pulled into some stretched-out configuration.”

“But this picture of the corpusants has them just at the mast-heads and yard-arms, not all over the boat.”

“That’s where the ‘concentrated’ word come in. I puzzled over that, too, when I first looked into the phenomenon. Made no sense.”

“Yeah. If the electrons are repelling each other they ought to spread out as much as possible. So why do they seem pour out of the pointy parts?”

“That was a mystery until the 1880s when Heaviside cleaned up Maxwell’s original set of equations. The clarified math showed that the key is the electric field’s spread-out-ness, technically known as divergence.”

With my finger I draw in the frost on his gelato cabinet. “Imagine this is a brass ball, except I’ve pulled one side of it out to a cone. Someone’s loaded it up with extra electrons so it’s carrying a high negative charge.”

“The electrons have spread themselves evenly over the metal surface, right, including at the pointy part?”

“Yup, that’s why I’m doing my best to make all these electric field arrows the same distance apart at their base. They’re also supposed to be perpendicular to the surface. What part of that field will put the most rip-apart stress on the local air molecules?”

“Oh, at the tip, where the field spreads out most abruptly.”

“Bingo. What makes the glow isn’t the average field strength, it’s how drastically the field varies from one side of a molecule to the other. That’s what rips them apart. And you get the greatest divergence at the pointy parts like at the Pequod’s mast-head.”

A beautiful April day, far too nice to be inside working. I’m on a brisk walk toward the lake when I hear puffing behind me. “Hey, Moire, I got questions!”

“Of course you do, Mr Feder. Ask away while we hike over to watch the geese.”

“Sure, but slow down , will ya? I been reading this guy’s blog and he says some things I wanna check on.”

I know better but I ask anyhow. “Like what?”

“Like maybe the planets have different electrical charges so if we sent an astronaut they’d get killed by a ginormous lightning flash.”

“That’s unlikely for so many reasons, Mr Feder. First, it’d be almost impossible for the Solar System to get built that way. Next, it couldn’t stay that way if it had been. Third, we know it’s not that way now.”

“One at a time.”

“OK. We’re pretty sure that the Solar System started as a kink in a whirling cloud of galactic dust. Gravity spanning the kink pulled that cloud into a swirling disk, then the swirls condensed to form planets. Suppose dust particles in one of those swirls, for whatever reason, all had the same unbalanced electrical charge.”

“Right, and they came together because of gravity like you say.”

I pull Old Reliable from its holster. “Think about just two particles, attracted to each other by gravity but repelled by their static charge. Let’s see which force would win. Typical interstellar dust particles run about 100 nanometers across. We’re thinking planets so our particles are silicate. Old Reliable says they’d weigh about 2×10 –18 kg each, so the force of gravity pulling them together would be … oh, wait, that’d depend on how far apart they are. But so would the electrostatic force, so let’s keep going. How much charge do you want to put on each particle?”

“The minimum, one electron’s worth.”

“Loading the dice for gravity, aren’t you? Only one extra electron per, umm, 22 million silicon atoms. OK, one electron it is … Take a look at Old Reliable’s calculation. Those two electrons push their dust grains apart almost a quintillion times more strongly than gravity pulls them together. And the distance makes no difference — close together or far apart, push wins. You can’t use gravity to build a planet from charged particles.”

“Sure, which is why I said almost impossible. Now for the second reason the astronaut won’t get lightning-shocked — the solar wind. It’s been with us since the Sun lit up and it’s loaded with both positive- and negative-charged particles. Suppose Venus, for instance, had been dealt more than its share of electrons back in the day. Its net-negative charge would attract the wind’s protons and alpha particles to neutralize the charge imbalance. By the same physics, a net-positive planet would attract electrons. After a billion years of that, no problem.”

“All right, what’s the third reason?”

“Simple. We’ve already sent out orbiters to all the planets. Descent vehicles have made physical contact with many of them. No lightning flashes, no fried electronics. Blows my mind that our Cassini mission to Saturn did seven years of science there after a six-year flight, and everything worked perfectly with no side-trips to the shop. Our astronauts can skip worrying about high-voltage landings.”

“Hey, I just noticed something. Those F formulas look the same.” He picks up a stick and starts scribbling on the dirt in front of us. “You could add them up like F=(Gm1m2+k0q1q2)/r2. See how the two pieces can trade off if you take away some mass but add back some charge? How do we know we’ve got the mass-mass pull right and not mixed in with some charge-charge push?”

“Good question. If protons were more positive than electrons, electrostatic repulsion would always be proportional to mass. We couldn’t separate that force from gravity. Physicists have separately measured electron and proton charge. They’re equal (except for sign) to 10 decimal places. Unfortunately, we’d need another 25 digits of accuracy before we could test your hypothesis.”

“OK. First we got the movie’s lightwave. The ray’s running along that black arrow, see? Some electron back behind the picture is going up and down to energize the ray and that makes the electric field that’s in red that makes other electrons go up and down, right?”

“That’s the red arrow, hmm?”

“Yeah, that electron got goosed ’cause it was standing in the way. It follows the electric field’s direction. Now help me out with the magnetic stuff.”

“Alright. The blue lines represent the lightwave’s magnetic component. A lightwave’s magnetic field lines are always perpendicular to its electric field. Magnetism has no effect on uncharged particles or motionless charged particles. If you’re a moving charged particle, say an electron, then the field deflects your trajectory.”

“This is what I’m still trying to wrap my head around. You say that the field’s gonna push the particle perpendicular to the field and to the particle’s own vector.”

“That’s exactly what happens. The green line, for instance, could represent an electron that crossed the magnetic field. The field deflected the electron’s path upwards, crossways to the field and the electron’s path. Then I suppose the electron encountered the reversed field from the lightwave’s following cycle and corrected course again.”

“And the grey line?”

“That’d be an electron crossing more-or-less along the field. According to the Right Hand Rule it was deflected downward.”

“Wait. We’ve got two electrons on the same side of the field and they’re deflected in opposite directions then correct back. Doesn’t that average out to no change?”

“Not quite. The key word is mostly. Like gravity fields, electromagnetic fields get weaker with distance. Each up or down deflection to an electron on an outbound path will be smaller than the previous one so the ‘course corrections’ get less correct. Inbound electrons get deflected ever more strongly on the way in, of course, but eventually they become outbound electrons and get messed up even more. All those deflections produce an expanding cone of disturbed electrons along the path of the ray.”

“Hey, but when any electron moves that changes the fields, right? Wouldn’t there be a cone of disturbed field, too?”

“Absolutely. The whole process leads to several kinds of dispersion.”

“Like what?”

“The obvious one is simple geometry. What had been a simple straight-line ray is now an expanding cone of secondary emission. Suppose you’re an astronomer looking at a planet that’s along that ray, for instance. Light’s getting to you from throughout the cone, not just from the straight line. You’re going to get a blurred picture.”

“What’s another kind?”

“Moving those electrons around extracts energy from the wave. Some fraction of the ray’s original photons get converted to lower-energy ones with lower frequencies. The net result is that the ray’s spectrum is spread and dispersed towards the red.”

“You said several kinds.”

“The last one’s a doozy — it affects the speeds of light.”

“‘Speeds,’ plural?”

“There’s the speed of field’s ripples, and there’s the speed of the whole signal, say when a star goes nova. Here’s a picture I built on Old Reliable. The gold line is the electric field — see how the ripples make the red electron wobble? The green dots on the axis give you comparison points that don’t move. Watch how the ripples move left to right just like the signal does, but at their own speed.”

“Which one’s Einstein’s?”

“The signal. Its speed is called the group velocity and in space always runs 186,000 mph. The ripple speed, technically it’s the phase velocity, is slower because of that extracted-and-redistributed-energy process. Different frequencies get different slowdowns, which gives astronomers clues about the interstellar medium.”

“It’s worse than that, Vinnie.” I pull out Old Reliable, my math-monster tablet. “Let me scan in that three-electron drawing of yours.”

“Good enough to keep a record of it?”

“Nope, I want to exercise a new OVR app I just bought.”

“You mean OCR.”

“Uh-uh, this is Original Vector Reconstruction, not Optical Character Recognition. OCR lets you read a document into a word processor so you can modify it. OVR does the same thing but with graphics. Give me a sec … there. OK, look at this.”

“Cool, you turned my drawing 180°, sort of. Nice app. Oh, and you moved the red electron’s path so it’s going opposite to the blue electron instead of parallel to the magnetic field. Why’d you bother?”

“Well, actually, they’re going in exactly the right direction for that, because a magnetic field pushes along perpendiculars. Ever hear of The Right Hand Rule?”

“You mean like ‘lefty-loosey, righty-tighty’?”

“That works, too, but it’s not the rule I’m talking about. If you point your thumb in the direction an electron is moving, and your index finger in the direction of the magnetic field, your third finger points in the deflection direction. Try it.”

“Hurts my wrist when I do it for the blue one, but yeah, the rule works for that. It’s easier for the red one. OK, you got this rule, fine, but why does it work?”

“Part of it goes back to the vector math you don’t want me to throw at you. Let’s just say that there are versions of a Right Hand Rule all over physics. Many of them are essentially definitions, in the same way that Newton’s Laws of Motion defined force and mass. Suppose you’re studying the movements directed by some new kind of force. Typically, you try to define some underlying field in such a way that you can write equations that predict the movement. You haven’t changed Nature, you’ve just improved our view of how things fit together.”

“So you’re telling me that whoever made that drawing I copied drew the direction those B-arrows pointed just to fit the rule?”

“Almost. The intensity of the field is whatever it is and the lines minus their pointy parts are wherever they are. The only thing we can set a rule for is which end of the line gets the arrowhead. Make sense?”

“I suppose. But now I got two questions instead of the one I come in here with. I can see the deflection twisting that electron’s path into a spiral. But I don’t see why it spirals upward instead of downward, and I still don’t see how the whole thing works in the first place.”

“I’m afraid you’ve stumbled into a rabbit hole we don’t generally talk about. When Newton gave us his Law of Gravity, he didn’t really explain gravity, he just told us how to calculate it. It took Einstein and General Relativity to get a deeper explanation. See that really thick book on my shelf over there? It’s loaded with tables of thermodynamic numbers I can use to calculate chemical reactions, but we didn’t start to understand those numbers until quantum mechanics came along. Maxwell’s equations let us calculate electricity, magnetism and their interaction — but they don’t tell us why they work.”

“I get the drift. You’re gonna tell me it goes up because it goes up.”

“That’s pretty much the story. Electrons are among the simplest particles we know of. Maxwell and his equations gave us a good handle on how they behave, nothing on why we have a Right Hand Rule instead of a Left Hand Rule. The parity just falls out of the math. Left-right asymmetry seems to have something to do with the geometry of the Universe, but we really don’t know.”

“Will string theory help?”

“Physicists have spent 50 years grinding on that without a testable result. I’m not holding my breath.”

Rumpus in the hallway. Vinnie dashes into my office, tablet in hand and trailing paper napkins. “Sy! Sy! I figured it out!”

“Great! What did you figure out?”

“You know they talk about light and radio being electromagnetic waves, but I got to wondering. Radio antennas don’t got magnets so where does the magnetic part come in?”

“19th-Century physicists struggled with that question until Maxwell published his famous equations. What’s your answer?”

“Well, you know me — I don’t do equations, I do pictures. I saw a TV program about electricity. Some Danish scientist named Hans Christian Anderson—”

“Ørsted.”

“Whoever. Anyway, he found that magnetism happens when an electric current starts or stops. That’s what gave me my idea. We got electrons, right, but no magnetrons, right?”

“Mmm, your microwave oven has a vacuum tube called a magnetron in it.”

“C’mon, Sy, you know what I mean. We got no whatchacallit, ‘fundamental particle’ of magnetism like we got with electrons and electricity.”

“I’ll give you that. Physicists have searched hard for evidence of magnetic monopoles — no successes so far. So why’s that important to you?”

“It told me that the magnetism stuff has to come from what electrons do. And that’s when I came up with this drawing.” <He shoves a paper napkin at me.> “See, the three balls are electrons and they’re all negative-negative pushing against each other only I’m just paying attention to what the red one’s doing to the other two. Got that?”

“Sure. The arrow means the red electron is traveling upward?”

“Yeah. Now what’s that moving gonna do to the other two?”

“Well, the red’s getting closer to the yellow. That increases the repulsive force yellow feels so it’ll move upward to stay away.”

“Uh-huh. And the force on blue gets less so that one’s free to move upward, too. Now pretend that the red one starts moving downward.”

“Everything goes the other way, of course. Where does the magnetism come in?”

“Well, that was the puzzle. Here’s a drawing I copied from some book. The magnetic field is those Barrows and there’s three electrons moving in the same flat space in different directions. The red one’s moving along the field and stays that way. The blue one’s moving slanty across the field and gets pushed upwards. The green one’s going at right angles to B and gets bent way up. I’m looking and looking — how come the field forces them to move up?”

“Good question. To answer it those 19th Century physicists developed vector analysis—”

Plane-polarized electromagnetic waveElectric (E) field is redMagnetic (B) field is blue(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)

“Don’t give me equations, Sy, I do pictures. Anyway, I figured it out, and I did it from a movie I got on my tablet here. It’s a light wave, see, so it’s got both an electric field and a magnetic field and they’re all sync’ed up together.”

“I see that.”

“What the book’s picture skipped was, where does the B-field come from? That’s what I figured out. Actually, I started with where the the light wave came from.”

“Which is…?”

“Way back there into the page, some electron is going up and down, and that creates the electric field whose job is to make other electrons go up and down like in my first picture, right?”

“OK, and …?”

“Then I thought about some other electron coming in to meet the wave. If it comes in crosswise, its path is gonna get bent upward by the E-field. That’s what the blue and green electrons did. So what I think is, the magnetic effect is really from the E-field acting on moving electrons.”

“Nice try, but it doesn’t explain a couple of things. For instance, there’s the difference between the green and blue paths. Why does the amount of deflection depend on the angle between theB direction and the incoming path?”

“Dunno. What’s the other thing?”

“Experiment shows that the faster the electron moves, the greater the magnetic deflection. Does your theory account for that?”

“Uhh … my idea says less deflection.”

“Sorry, another beautiful theory stumbles on ugly facts.”

~~ Rich Olcott

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